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The Most Common Errors in Undergraduate Mathematics (2009)

math.vanderbilt.edu

11–20 of 161 posts

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#11
post #5

Bad handwriting. At age 40 I started taking a masters in stats and had situations where I had exponents on exponents. This lead me to buy a higher resolution tablet for reading pdf's with tiny math. I also bought a finer point pen and this helped me improve my handwriting a lot . Closing loops on "o's" or backtracing the upward line of a cursive "t" to not make a loop. With the finer point, I was able to see my impre…

I stopped handwriting math to turn in my freshman year of college, LaTex was just too good looking.

that seems like a ton of work, especially for problem sets

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#12
post #5

Bad handwriting. At age 40 I started taking a masters in stats and had situations where I had exponents on exponents. This lead me to buy a higher resolution tablet for reading pdf's with tiny math. I also bought a finer point pen and this helped me improve my handwriting a lot . Closing loops on "o's" or backtracing the upward line of a cursive "t" to not make a loop. With the finer point, I was able to see my impre…

I stopped handwriting math to turn in my freshman year of college, LaTex was just too good looking.

Extra fine Japanese fountain pens are the solution to all your problems.

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#13
post #4

When I was in undergrad, I declared a math minor quite late - just before my junior year. This led to me taking up to 9 hours of math credits in a semester. The reason I declared my math minor was because I was interested in going for a PhD in economics and my econ professors all recommended that I try to take as many math classes as possible to prepare. Reader, I was not a 'numbers person' at all. However, in all of…

> I would go to office hours and the teachers were seriously so helpful. As a grad student that taught undergrads I always encouraged students to attend office hours. Most instructors do want you to succeed and one-on-one time is one of the best ways to learn. Definitely take advantage of your instructors' office hours; ask questions about anything that you aren't 100% sure about!

> I would go to office hours and the teachers were seriously so helpful. This was the only way I survived. I learned that you don't have to be a 'numbers person' at all to be good at math. You just have to understand what's going on under the hood, and this may require lots of questions and outside help. But most importantly, you just have to practice

I agree with all of this and it's how I got through extensive math. I'm not a "natural" at math and I'm not sure that really exists or possibly very people that are. I made sure to get to the office hours and I was surprised that there was almost no one there most of the time. I figured the cost of tuition is best justified by using as many hours of one-on-one time with an expert in the subject to better understand it yourself.

And to your last point about practice, I can't emphasize this enough. I would do the same problem sets over and over until I had them down. And it wasn't just memorizing the steps but rather getting to the point of being able to recognize the pattern. This made math "easy" at that point which is a weird phenomenon. Something that seemed so confusing and impossible suddenly becomes "easy". And then you can move on to the next step.

I understand rote learning is not popular because it is painful. But I do believe "drilling it in" over and over gets the job done. But it takes the will and the effort. It's been a long time but I think I could still solve most the math I took back then.

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#14
post #5

Bad handwriting. At age 40 I started taking a masters in stats and had situations where I had exponents on exponents. This lead me to buy a higher resolution tablet for reading pdf's with tiny math. I also bought a finer point pen and this helped me improve my handwriting a lot . Closing loops on "o's" or backtracing the upward line of a cursive "t" to not make a loop. With the finer point, I was able to see my impre…

This right here was such an infuriating discovery for me. Math never made sense to me until I had a kindly old teacher who insisted she watch me write out every step of a problem (in community college). She pointed out that the logic was fine, I was just being sloppy with my notes which led to errors.

It was like a dam broke over night. Everything clicked and I was so pissed off that it took so long to find such a stupid issue. Better late than never I suppose...

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#16
post #10

Mathematical notation is terrible. I don't mean this in the usual "we need to invent new symbols to make it clearer" way. I mean it in the way that it has implicit typing that gets coerced constantly. Using Haskell types D :: (R -> R) -> (R -> R). Yet it gets used on things like D 2 = 0 which implies D :: (R -> R). What you've actually done is an implicit conversion of 2 :: R to 2(x) = 2 :: R -> R and 0 is not 0::R i…

That's not a very convincing example, given that numeric literals are polymorphic in Haskell.

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#17
post #5

Bad handwriting. At age 40 I started taking a masters in stats and had situations where I had exponents on exponents. This lead me to buy a higher resolution tablet for reading pdf's with tiny math. I also bought a finer point pen and this helped me improve my handwriting a lot . Closing loops on "o's" or backtracing the upward line of a cursive "t" to not make a loop. With the finer point, I was able to see my impre…

I wish someone had forced me to learn LaTeX back in high school.

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#18
post #5

Bad handwriting. At age 40 I started taking a masters in stats and had situations where I had exponents on exponents. This lead me to buy a higher resolution tablet for reading pdf's with tiny math. I also bought a finer point pen and this helped me improve my handwriting a lot . Closing loops on "o's" or backtracing the upward line of a cursive "t" to not make a loop. With the finer point, I was able to see my impre…

When I was 9 I failed some question about fractions because I saw one 6 and it was just a bad written 5.

At that age it took me a while to understand where the problem was and too late to ask my teacher to reconsider it.

Well, was so intense that I remember it until today, 30 and some years later.

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#19
post #16
post #10

Mathematical notation is terrible. I don't mean this in the usual "we need to invent new symbols to make it clearer" way. I mean it in the way that it has implicit typing that gets coerced constantly. Using Haskell types D :: (R -> R) -> (R -> R). Yet it gets used on things like D 2 = 0 which implies D :: (R -> R). What you've actually done is an implicit conversion of 2 :: R to 2(x) = 2 :: R -> R and 0 is not 0::R i…

That's not a very convincing example, given that numeric literals are polymorphic in Haskell.

Not all Haskell is GHC, though

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#20
post #10

Mathematical notation is terrible. I don't mean this in the usual "we need to invent new symbols to make it clearer" way. I mean it in the way that it has implicit typing that gets coerced constantly. Using Haskell types D :: (R -> R) -> (R -> R). Yet it gets used on things like D 2 = 0 which implies D :: (R -> R). What you've actually done is an implicit conversion of 2 :: R to 2(x) = 2 :: R -> R and 0 is not 0::R i…

So you say we should specify when 2 means number two and when it means the constant function? How does it help?
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